Result:
Understanding the Harmonic Mean
The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of a set of values. It is often used in scenarios where rates are involved, such as in calculating average speed or price per unit.
Formula: \( \text{Harmonic Mean} = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \)
Real-Life Example
Suppose you want to find the average speed for a trip where you traveled 60 km at 30 km/h and another 60 km at 60 km/h. Using the harmonic mean gives a more accurate representation of average speed when distances are the same but speeds vary.
Calculation: \( \text{Harmonic Mean} = \frac{2}{\frac{1}{30} + \frac{1}{60}} = 40 \, \text{km/h} \)